Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Understanding an integral rule.

  1. Jul 22, 2015 #1
    Hi I'm tying to understand notations in Integration, and would really appreciate some help making sure that my understanding is right.


    My books writes

    Let u and v be functions of x whose domains are an open interval I, and suppose du and dv exist for every x in I.


    Then it defines

    1) ∫(du)= u + C
    2) ∫(c*du) = c*∫(du)


    and
    3) ∫(cos(u)du = sin u +C


    Now i do understand the first 2, but I want to make sure i understand the 3rd rule.

    If u is a function of x with the equation u(x)=x^2

    Then the derivative
    du/dx= 2x

    The differential
    du=u'(x)dx

    Now if it's true that du=u'(x)dx
    Then it does make sense that ∫du =u+C because ∫du=∫u'(x)*dx and the integral of the derivative if u is u.

    But if u=x^2

    Then ∫(cos(x^2)*du = ∫(cos(x^2)*(2x)dx and this is = sin(x^2) + C as the statement above says.
    because the derivative of sin(x^2) = cos(x^2)*(2x).

    Is this the right interpretation?
     
    Last edited: Jul 22, 2015
  2. jcsd
  3. Jul 22, 2015 #2
    why is ∫(cos(x^2)*(2x)dx not equal to sin(x^2) + C? you said in the line below it that
    which is exactly what appears under the integral sign.
     
  4. Jul 22, 2015 #3
    Oh forgive me, that NOT was a BIG mistake ;)
    You are right, it is e equal to it.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Understanding an integral rule.
Loading...